Alliterative Name: Peter Parker, Bruce Banner, Reed Richards... the list goes on. Justified, in that Stan was working on more than a dozen comics at any given time when he created those names, and the alliteration served as a mnemonic. Sometimes it didn't work, which is why the Hulk's full name is "Robert Bruce Banner," and why an early issue of Amazing Spider-Man listed Peter Parker as "Peter Palmer". This was parodied in an episode of The Big Bang Theory.
He even had this in real life with his brother Larry Lieber.
In Heroman, Stan appears as a patron in the restaurant Joey works at who's always drinking coffee.
He originally created J. Jonah Jameson so there would be a character he could play in an adaptation, which ended up never happening despite the numerous adaptations featuring him.
City of Weirdos: Stan uses this one a lot. If something weird is going on in midtown Manhattan, count on seeing a jaded New Yorker who's certain that it's someone filming a movie or "some nutty publicity stunt."
Comic Book Time: Lee was in charge when Marvel first began to abandon its real-time storytelling in favour of "Marvel time" in 1968. The statement that comics do not represent change, but "the illusion of change" is usually attributed to either him or Marv Wolfman.
Cool Old Guy: So much so that he is the page's image.
Cool Shades: One really can't imagine Stan the man without his dark specs.
Creator Cameo: Stan has always enjoyed this trope, both in the comics themselves and elsewhere. It's been joked that he has the superpower to appear in any media, so observe:
He's appeared in a number of Marvel Comics as himself:
Most famously, Stan showed up at the wedding of Reed Richards and Sue Storm with Jack Kirby — only to be denied entry!
Stan showed up (with artist Stan Goldberg) in one Millie the Model story, as the creators of a comic book starring Millie.
A series of 2006 one-shots called Stan Lee Meets (e.g. Stan Lee Meets the Thing, Stan Lee Meets Doctor Doom, etc.) was built around this trope.
He has contractually-obliged cameos in every movie based on one of his works, and usually appears in Marvel movies he isn't contractually obliged to get cameos in. As for his cameos:
Spider-Man: In 1, a heroic bystander who saves a kid from falling debris. In 2, another bystander. In 3, a bystander who poetically muses about Spider-Man to Peter in the beginning.
Hulk: A security guard getting into an elevator with Lou Ferrigno.
The Incredible Hulk: The civilian who is poisoned by Banner's irradiated blood in the beginning.
Daredevil: A man reading a newspaper who almost walks out into traffic only to be stopped by the blind kid Matt Murdock.
Fantastic Four: Willie Lumpkin, the Baxter Building's mailman. In Rise of the Silver Surfer he plays himself trying to get into the wedding, a Call Back to the same thing in the actual comics.
Iron Man: He plays a person who was mistaken for Hugh Hefner by Tony. In 2 he is mistaken for Larry King. Whether he is actually supposed to be these people is unknown.
Thor: He plays a New Mexico local with a truck trying to pull Mjolnir from its spot. Credited as Stan the Man.
Captain America: The First Avenger: He plays an Army general in a crowd who loses the opportunity to see Rogers because he left on another mission, but mistakes the messenger for Capt. "I thought he'd be taller." This is a semi-exception as, while Lee didn't create the character, he did create Cap's trademark move of throwing his shield in a text story in the 1940s. (He also did some writing for the comic, and he's the one who brought Cap back into the Marvel Universe in the 1960s and added him to The Avengers.)
X-Men: In the first film, he appears as a random beachgoer who watches Senator Kelly emerging from the ocean. In the third film, he appears in the beginning of the film as a neighbor of a young Jean Grey watering his lawn (a scene in which fellow X-Men writer Chris Claremont also cameos).
The Avengers: Near the end of the film, Stan shows up as a man playing chess in the park, who is interviewed by a news crew regarding the events of the movie's finale.
He appears as himself in the series finale of Spider-Man: The Animated Series when Madam Web brings together several Spider-Mans from alternate universes, one of whom is an actor who plays him in the real world.
Historical Villain Upgrade: Frequently gets this from partisans of co-creators like Jack Kirby and Steve Ditko — though admittedly he's never been good at sharing credit (then again, neither were Kirby and Ditko).
In Case You Forgot Who Wrote It: "Stan Lee Presents" appeared on all Marvel issue titles for decades (because he was Marvel's publisher at that time, though not a writer except for the occasional special project).
Jerkass: Stan often portrays himself as a bit of a Jerkass in comics where "Stan Lee" is a character. Stan has also said (presumably at least somewhat in jest) that he based legendary Jerkass J. Jonah Jameson on himself. He was also kind of crusty when he appeared on The Big Bang Theory.
Taken to its logical conclusion where he's the big bad of Ultimo.
And then there's his role as "principal Stanley" in Mini Marvels, where once Spidey starts angsting — justifiably — about his status as a Butt Monkey, causes Stan to look awkward once he mentions "who decided this to happen to me?".
Ascends in X-Play, where "Roger the Stan Lee Experience" recounts tales of doing Jack Kirby's wife and stealing credit for Kirby's success.
Kid Sidekick: He doesn't like the trope and has likened it to endangerment of minors — hence the death of Bucky Barnes. He totally subverts this trope later on with Johnny Storm being a team member rather than just a sidekick. And, ultimately, Spider-Man being the first lone teen super hero of his kind. He also admits how hypocritical this is.
The Nicknamer: Responsible for nicknaming the majority of the Marvel Bullpen and characters.
Purple Prose: A peerlessly pounding pantheon of pulse-poundingly purple prose! Nobody does it better, true believers!
Self-Deprecation: Many times. See Jerkass above. He also appeared in an episode of The Simpsons, where he acts like a Cloudcuckoolander — or, as Comic Book Guy put it, "I am starting to suspect his mind is no longer in mint condition."
Take That: In his Just Imagine series, he makes Robin a bad guy. Knowing how he hates sidekicks, doing that to the character that popularized comic book sidekicks would seem more like this than just trying to make him a complex character.
Villain Decay: While his heroes and writing style are still iconic today, his storytelling style is also somewhat infamous for really introducing a lot of this to Marvel villains — he'd have them say things like "This time my brilliant plan will destroy those meddling heroes!!!" without any sense of irony, even after the villain listed all the times they'd already gotten stomped. In the early 60's, it still kind of worked; by 1969 or so, not so much. Much of his own later work — not to mention a great deal of comicry that followed in his footsteps — had to spend time fighting the villainous cliches he himself constructed.